In electronic or hybrid imaging systems where the input comprises either stationary images or time-varying image sequences, it may be desired to subject these images or image sequences to static or dynamic spatial interpolation (pan or zoom). The interpolation may be required for spatial standards conversion, for image magnification within a fixed spatial standard, or other applications.
In general, spatial interpolation is achieved by means of a low-pass filter which attenuates all frequencies above the nyquist frequency of the output signal (anti-aliasing) whilst maximising pass-band response and enables a variable phase-shift of the output signal with respect to the input signal. In the case of dynamic zoom, since the zoom ratio varies from frame-to-frame, it is also required that the cut-off frequency of the interpolation filter be easily adjustable.
A control parameter, zoom ratio, R, can be defined as the quotient of m/n where m is the pixel length of the output from a spatial interpolation unit, and n is the pixel length corresponding to a particular image feature input to the spatial interpolation unit, m and n being measured to sub-pixel accuracy. The definition of this control parameter holds for both image magnification within a fixed spatial standard and for spatial standards conversion. The cut-off frequency of each filter, described in terms of a fraction of the input nyquist frequency, is therefore defined to be equal to the zoom ratio.
In some applications where speed is not a limiting factor, it may be possible to generate the interpolation filter coefficients for the zoom ratio required for each image frame in-situ. Two possible methods can be used to achieve this as is well known:
1) using a windowed sinc function (Digital Image Processing, W K Pratt, Wiley-InterScience, pages 291 to 295) as a continuous or sampled impulse response. The window width (Hamming window is often preferred) defines the number of filter taps, and the cut-off frequency is defined by the width of the sinc function.
2) using an optimisation method to generate a low-pass filter with variable cut-off frequency and stop- and pass-band performance, for example, the Remez Exchange Algorithm (Theory and Application of Digital Signal Processing, Rabiner and Gold, Prentice-Hall 1975, pages 136 to 140).